Scotland Yard confirmed it was considering a complaint that McNulty may have "obtained pecuniary advantage by deception".

In March, it emerged that McNulty had claimed about £60,000 from Commons allowances since 2002 towards maintaining a house where his parents lived.

He was able to receive the money because the property - which he owns - is in his Harrow constituency, just 11 miles from parliament.

The MP lives with his wife in her house three miles from Westminster, but insisted he had not broken any rules because he sometimes did work at the Harrow property.

However, he also told the Mail on Sunday in March that he had stopped claiming the second home allowance of up to £24,000 a year, and called for MPs who live within 60 miles of parliament to be banned from getting it.

The Commons voted last week to give members with Greater London constituencies a £7,500 annual "weighting" payment rather than letting them claim for second homes.

A police spokesman said: "We have received a complaint from a member of the public and we are considering the allegation."

A spokesman for McNulty stressed that an investigation was not underway. He said: "There is no police investigation. We believe the police have confirmed that they have received a complaint."